An image compression coding technique involves transforming the image into another domain with Curvelet function and then quantizing the coefficients with modified Set Partitioning In Hierarchical Trees algorithm (SPIHT) has been presented in this paper. Curve functions are effective in representing functions that have discontinuities along straight lines. Normal Wavelet transforms fail to represent such functions effectively. SPIHT has been defined for normal wavelet decomposed images as an embedded quantization process. If the coefficients obtained from Curvelet transform of the image with more discontinuities along straight lines have to subject to quantization process with SPIHT, the existing structure of the SPIHT should be modified to suit with the output of the Fast Curvelet Transform (FCT).